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Boundary behavior of functions from Sobolev classes defined on domains with exterior peak

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Abstract

We establish an invertible characteristic of the boundary behavior of functions from Sobolev spaces defined on a space domain having a vertex of exterior peak on the boundary. The boundary is assumed sufficiently smooth in a neighborhood of the peak vertex. The description of the traces on the boundary is given with the use of weighted Besov spaces.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, 630073, Russia

    I. M. Pupyshev & M. Yu. Vasil’chik

Authors
  1. I. M. Pupyshev
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  2. M. Yu. Vasil’chik
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Correspondence to I. M. Pupyshev.

Additional information

Original Russian Text © I. M. Pupyshev and M. Yu. Vasil’chik, 2014, published in Matematicheskie Trudy, 2014, Vol. 17, No. 1, pp. 70–98.

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Pupyshev, I.M., Vasil’chik, M.Y. Boundary behavior of functions from Sobolev classes defined on domains with exterior peak. Sib. Adv. Math. 24, 261–281 (2014). https://doi.org/10.3103/S1055134414040038

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  • DOI: https://doi.org/10.3103/S1055134414040038

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